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Mathematics Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach (Courant Lecture Notes)
Posted on 2010-04-16
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Author: Percy Deift
Publisher: American Mathematical Society (2000) Binding: Paperback, 261 pages pricer: $33.00 ISBN-10: 0821826956 editorialreviews This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random $n {\times} n$ matrices exhibit universal behavior as $n {\rightarrow} {\infty}$? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
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